Of the three independent events E_1, E_2 and E_3 the probability that only E_1 occurs is \alpha only E_2 occurs is \beta and only E_3 occurs is \gamma . Let the probability p that none of events E_1, E_2 or E_3 occurs satisfy the equations (\alpha - 2\beta)p = \alpha \beta and (\beta - 3\gamma ) p = 2\beta \gamma . All the given probabilities are assumed to lie in the interval (0 , 1). Then { \text{Probability of occurrence of} E_1} / {\text{Probability of occurrence of} E_3} = [JEE Adv 2013 P1]

Probability

Section: Mathematics

Question : 40 of 52

Marks: +1, -0

Of the three independent events E1,E2 and E3 the probability that only E1 occurs is α only E2 occurs is β and only E3 occurs is γ . Let the probability p that none of events E1,E2 or E3 occurs satisfy the equations (α−2β)p = αβ and (β−3γ) p = 2βγ . All the given probabilities are assumed to lie in the interval (0 , 1). Then

Probability of occurrence of‌E1

Probability of occurrence of‌E3

[JEE Adv 2013 P1]

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